Computational Methods for Multiscale Analysis and Design of Nonlinear Multifunctional Materials and Structures for Energy Management

Managing energy transfer in a system through arrangement of different material media is an essential component of the engineering design process. For example, in protective structures designed for impact mitigation, energy can be dissipated by arranging the underlying material to experience inelastic behavior. Additionally, energy transfer in materials can be engineered by purposefully designing sub-scale features, resulting in the development of novel engineered materials with unprecedented stiffness to weight ratios, remarkable vibration and sound control, and unparalleled coupling of electromagnetic and mechanical effects. Increasing computational capabilities have led to widespread use of numerical simulations to better predict energy transfer mechanisms within detailed arrangements of material media at different scales. These simulations also provide the basis through which the inverse problem of achieving superior control over energy transfer through optimized material arrangements can be approached. The proliferation of increasingly sophisticated simulations also coincides with the rapid digitization of fabrication processes driven by additive manufacturing methods which approach ever smaller scales and finer geometrical details. To take advantage of these advances, computational design frameworks rooted in advanced simulation and optimization methods are needed.

The focus of this dissertation is on development of numerical methods for the analysis and design of materials and structures which can be used to better manage different energy transfer mechanisms. This development concerns two areas: (a) A rational design framework for energy dissipating structures based on topology optimization and accounting for the complex interplay between physical phenomena such as inelastic mechanisms, material rate effects, large deformations, and inertia effects. (b) Multiscale simulation approaches for nonlinear, transient, and multiphysics phenomena involved in energy transfer, and the application of these simulation techniques to the design optimization of engineered materials. It is envisioned that that the developed numerical methods will help lay the groundwork for seamless integration of computational simulation, design, and fabrication frameworks to realize the next generation of functionally optimal structures and materials for energy management.